Phase-dependent noise correlations in normal-superconducting structures

Abstract

We study nonequilibrium noise correlations in diffusive normal-superconducting structures in the presence of a supercurrent. We present a parametrization for the quasiclassical Green's function in the first order of the counting field χ. This we employ to obtain the voltage and phase dependence of cross and autocorrelations and to describe the role played by the setup geometry. We find that the low-voltage behavior of the effective charge q eff describing shot noise is a result of a competition between anticorrelation of Andreev pairs due to proximity effect and the depression of the local density of states. Furthermore, we show that the noise correlations are independent of the sign of the supercurrent.6 PACS numbers: 74.40.+k, 42.50.Lc, The charge transmitted through a disordered conductor in unit time varies due to the quantum nature of the transport process. This variation is characterized by the current distribution, whose width at low temperatures is directly related to the shot noise.1 In metallic conductors, the corrections induced by the quantum coherence on the current and conductance distributions are small, 2,3 but in a metal in contact to a superconductor, more pronounced effects may be observed, e.g., in the out-of-equilibrium noise experiments. 4,5,6,7 In the context of a normal-superconducting (NS) two-terminal setup, the theoretical endeavours have recently covered, e.g., the voltage dependence of the shot noise 8,9 and certain lowbias anomalies.9,10 Multiterminal structures have been discussed in the incoherent regime, 11,12,13,14 and in the presence of a supercurrent, in a short junction, 15 and for specific values of a phase difference in a three-terminal setup. The latter was described by a method based on a direct discretization of the equations governing the full counting statistics [see Eq. (1)]. 4In the presence of the superconducting proximity effect and at voltages of the order of E T /e, the effective charge q eff characterizing the magnitude of shot noise is lower than 2e, the value corresponding to a Cooper pair. 4,8,9Here E T = D/L 2 is the Thouless energy, with D the diffusion constant and L the wire length. Applying a supercurrent in a three-terminal structure (Fig. 1) allows one to study the nature of this proximity-induced change in q eff . For example, with this approach, we directly show that the lowering of q eff is due to a competition of anticorrelation effects induced by the superconducting proximity effect 4 and the depression of the local density of states.16 In principle, the effect of an extra current in the system would be twofold: to tune the coherent effects and to induce its own correlations. Here we show that within our noninteracting model supercurrent does only the previous as all the correlations in the system are independent of the supercurrent sign.The full counting statistics 17,18,19 has recently become the method of choice to calculate shot noise in diffusive mesoscopic conductors but, to our knowledge, the cross correlations in the presence of supercurre...

Gate-tunable zero-frequency current cross correlations of the quartet state in a voltage-biased three-terminal Josephson junction

“…In an experiment, the width in voltage (V a , V b ) parameter plane of the anomaly obtained for 0 /∆ < ∼ 1 in the cross-correlations is expected to correlate to the Josephson anomaly in the average current, because both anomalies originate from the appearance of the three-body phase variable ϕ Q = ϕ a +ϕ b −2ϕ c . It is noted finally that phase-sensitive noise was already calculated and measured in Andreev interferometers 30,31 . It is proposed here to go one step further and measure an anomaly in the noise or in the cross-correlations of a three-terminal Josephson junction.…”

Positive current cross-correlations in a highly transparent normal-superconducting beam splitter due to synchronized Andreev and inverse Andreev reflections

“…Finally, correlations between pairs of Andreev pairs were discussed 59,60 in connection with noise in an Andreev interferometer.…”

“…Finally, correlations between pairs of Andreev pairs were discussed 57,58 in connection with noise in an Andreev interferometer. Future studies of this class of setups might include the effect of arbitrary applied voltages and quantitative effects of three-dimensional geometry.…”